What is the value of (4sin(150))/6 ?

The value of (4sin(150))/6 is 1/3

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(4sin(150))/6

\frac{4 sin ( 15 0 ^{\circ} )}{6}

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

\frac{4 sin ( 15 0 ^{\circ} )}{6}

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{4 \cdot \frac{1}{2}}{6}

Simplify

\frac{4 \cdot \frac{1}{2}}{6} : \frac{1}{3}

\frac{4 \cdot \frac{1}{2}}{6}

Multiply

4 \cdot \frac{1}{2} : 2

4 \cdot \frac{1}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 4}{2}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2

= \frac{2}{6}

Cancel the common factor:

2

= \frac{1}{3}

= \frac{1}{3}

sin (32.0 1^{\circ})

csc (\frac{- 5 π}{3})

cos (\frac{π}{11})

cos (6 0^{\circ}) \cdot sin (3 0^{\circ})

2 \cdot cos^{2} (\frac{π}{2}) - 2 \cdot sin (\frac{π}{2})